Critical free energy and Casimir forces in rectangular geometries

Details Critical free energy and Casimir forces in rectangular geometries Critical free energy and Casimir forces in rectangular geometries

2010-12-29

arxiv.org/abs/1012.5955v2

Physics

Condensed Matter

Statistical Mechanics

23 pages, 14 figures

Scientific paper

We study the critical behavior of the free energy and the thermodynamic Casimir force in a $L_\parallel^{d-1} \times L$ block geometry in $2 1$), and zero for a cube $(\rho=1)$. We also present extrapolations to the cylinder limit ($\rho=\infty$) and to the film limit ($\rho=0$) for $n=1$ and $d=3$. Our analytic results for finite-size scaling functions in the minimal renormalization scheme at fixed dimension $d=3$ agree well with Monte Carlo data for the three-dimensional Ising model by Hasenbusch for $\rho=1$ and by Vasilyev et al. for $\rho=1/6$ above, at, and below $T_c$.

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